A computer-based method of measuring the integrated intensities of the reflections on the X-ray diffraction photograph of an oriented crystalline polymer

1987 ◽  
Vol 20 (3) ◽  
pp. 246-255 ◽  
Author(s):  
I. H. Hall ◽  
J. Z. Neisser ◽  
M. Elder
Keyword(s):  
Intensity Distribution ◽  
Statistical Tests ◽  
Structure Refinement ◽  
Intensity Variation ◽  
Crystalline Polymer ◽  
Background Intensity ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Photograph ◽  
Integrated Intensities

The method is designed to be used with a batch-processing computer system and will determine the integrated intensities of the spots on an X-ray diffraction photograph of an oriented fibre of a partially crystalline synthetic polymer. It is necessary to assume that the spot boundary is elliptical, that the intensity distribution along any line through the centre of this ellipse is Gaussian, and that the background intensity variation is linear over the region of a spot; these are justified experimentally, although, in the radial direction, the choice of a Gaussian intensity distribution is probably theoretically unsound. The computational procedures correct for minor differences between users in the choice of input parameters and reject bad choices. The method was applied to determine the intensities of the 30 visible spots in the diffraction photograph of oriented poly(trimethyleneterephthalate) which were used in a subsequent structure refinement. successful integrations were obtained for 22 spots, the failures being (1) pairs of similar intensity just resolved by eye, (2) better resolved pairs of which one member is stronger than the other, or (3) very weak. Statistical tests indicated very much better internal consistency of data than is usually obtained with these materials, and enabled a rational weighting scheme to be used in the structure refinement. The R factor of 7.9% obtained is unusually low, indicating much improved accuracy over earlier methods.

scholarly journals The role of an objective function in the mathematical modelling of wide-angle X-ray diffraction curves of semi-crystalline polymers

2021 ◽  
Vol 77 (6) ◽  
Author(s):  
Małgorzata Rabiej ◽  
Stanisław Rabiej
Keyword(s):  
Objective Function ◽  
Polyvinylidene Fluoride ◽  
Least Squares Method ◽  
Statistical Tests ◽  
Crystalline Polymer ◽  
Polyamide 6 ◽  
Wide Angle ◽  
X Ray Diffraction ◽  
X Ray

To decompose a wide-angle X-ray diffraction (WAXD) curve of a semi-crystalline polymer into crystalline peaks and amorphous halos, a theoretical best-fitted curve, i.e. a mathematical model, is constructed. In fitting the theoretical curve to the experimental one, various functions can be used to quantify and minimize the deviations between the curves. The analyses and calculations performed in this work have proved that the quality of the model, its parameters and consequently the information on the structure of the investigated polymer are considerably dependent on the shape of an objective function. It is shown that the best models are obtained employing the least-squares method in which the sum of squared absolute errors is minimized. On the other hand, the methods in which the objective functions are based on the relative errors do not give a good fit and should not be used. The comparison and evaluation were performed using WAXD curves of seven polymers: isotactic polypropylene, polyvinylidene fluoride, cellulose I, cellulose II, polyethylene, polyethylene terephthalate and polyamide 6. The methods were compared and evaluated using statistical tests and measures of the quality of fitting.

Algorithms of Two-Dimensional X-Ray Diffraction

MRS Advances ◽  
2016 ◽  
Vol 1 (26) ◽  
pp. 1921-1927
Author(s):  
Bob B. He
Keyword(s):  
Diffraction Pattern ◽  
Intensity Distribution ◽  
Structure Refinement ◽  
Azimuthal Angle ◽  
Bragg Angle ◽  
Phase Identification ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Diffraction Vector ◽  
X Ray

ABSTRACTX-ray diffraction pattern collected with two-dimensional detector contains the scattering intensity distribution as a function of two orthogonal angles. One is the Bragg angle 2θ and the other is the azimuthal angle about the incident x-ray beam, denoted by γ. A 2D diffraction pattern can be integrated to a conventional diffraction pattern and evaluated by most exiting software and algorithms for conventional applications, such as, phase identification, structure refinement and 2θ-profile analysis. However, the materials structure information associated to the intensity distribution along γ direction is lost through the integration. The diffraction vector approach has been approved to be the genuine theory in 2D data analysis. The unit diffraction vector used for 2D analysis is a function of both 2θ and γ. The unit diffraction vector for all the pixels in the 2D pattern can be expressed either in the laboratory coordinates or in the sample coordinates. The vector components can then be used to derive fundamental equations for many applications, including stress, texture, crystal orientation and crystal size evaluation.

scholarly journals The Radiation Transfer of Soft X-rays

1997 ◽  
Vol 166 ◽  
pp. 337-340 ◽  
Author(s):  
Jürgen Kerp ◽  
Jochen Pietz
Keyword(s):  
Power Law ◽  
Intensity Distribution ◽  
Galactic Halo ◽  
Background Radiation ◽  
Plasma Temperature ◽  
Intensity Variation ◽  
Background Intensity ◽  
X Rays ◽  
Energy Bands ◽  
X Ray

AbstractWe discuss the link between the halo plasma temperature and the power-law spectral index of the extragalactic background radiation. This link is of strong influence for the derivation of the Galactic halo intensity distribution. In principal, we can distinguish between two combinations of Galactic halo plasma temperature and power-law slope. The first combination consists of a halo plasma of Thalo = 106 K and an E−2 approximation of the extragalactic background radiation. The second combination is Thalo = 106.2 K and an E−1.5. Both combinations are in agreement with recent observational results, thus it is not feasible to discriminate between both models on the basis of X-ray data available. But, the soft X-ray background intensity distribution in the ¼ keV and ¾ keV ROSAT energy bands differs significantly. The Thalo = 106 K and an E−2 allows a patchy ¼ keV intensity distribution while the Thalo = 106.2 K and an E−1.5 predicts a much smoother intensity variation since the hotter halo plasma accounts for a significant fraction of the ¾ keV background radiation.

Materials characterization from diffraction intensity distribution in the γ-direction

2014 ◽  
Vol 29 (2) ◽  
pp. 113-117 ◽  
Author(s):  
Bob B. He
Keyword(s):  
Intensity Distribution ◽  
Crystal Size ◽  
Profile Analysis ◽  
Structure Refinement ◽  
Size Analysis ◽  
Phase Identification ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
X Ray ◽  
Orientation Relations

Two-dimensional X-ray diffraction (XRD2) pattern can be described by the diffraction intensity distribution in both 2θ and γ-directions. The XRD2 images can be reduced to two kinds of profiles: 2θ-profile and γ-profile. The 2θ-profile can be evaluated for phase identification, crystal structure refinement, and many applications with many existing algorithms and software. In order to evaluate the materials structure associated with the intensity distribution along γ-angle, either the XRD2 pattern should be directly analyzed or the γ-profile can be generated by 2θ-integration. A γ-profile contains information on texture, stress, crystal size, and crystal orientation relations. This paper introduces the concept and fundamental algorithms for stress, texture, and crystal size analysis by the γ-profile analysis.

Structure refinement of (Al, Zn)49Mg32-type phases by single-crystal X-ray diffraction

2000 ◽  
Vol 294-296 ◽  
pp. 327-330 ◽  
Author(s):  
W. Sun ◽  
F.J. Lincoln ◽  
K. Sugiyama ◽  
K. Hiraga
Keyword(s):  
Single Crystal ◽  
Structure Refinement ◽  
X Ray Diffraction ◽  
X Ray

Rare-earth crystal chemistry of thalénite-(Y) from different environments

2018 ◽  
Vol 82 (2) ◽  
pp. 313-327
Author(s):  
Markus B. Raschke ◽  
Evan J. D. Anderson ◽  
Jason Van Fosson ◽  
Julien M. Allaz ◽  
Joseph R. Smyth ◽  
...  
Keyword(s):  
Rare Earth ◽  
Rare Earth Element ◽  
Earth Element ◽  
Spatial Scales ◽  
Structure Refinement ◽  
X Ray Diffraction ◽  
Heavy Rare Earth ◽  
Heavy Rare Earth Element ◽  
X Ray ◽  
Golden Horn

ABSTRACTThalénite-(Y), ideally Y3Si3O10F, is a heavy-rare-earth-rich silicate phase occurring in granite pegmatites that may help to illustrate rare-earth element (REE) chemistry and behaviour in natural systems. The crystal structure and mineral chemistry of thalénite-(Y) were analysed by electron microprobe analysis, X-ray diffraction and micro-Raman spectroscopy from a new locality in the peralkaline granite of the Golden Horn batholith, Okanogan County, Washington State, USA, in comparison with new analyses from the White Cloud pegmatite in the Pikes Peak batholith, Colorado, USA. The Golden Horn thalénite-(Y) occurs as late-stage sub-millimetre euhedral bladed transparent crystals in small miarolitic cavities in an arfvedsonite-bearing biotite granite. It exhibits growth zoning with distinct heavy-rare-earth element (HREE) vs. light-rare-earth element (LREE) enriched zones. The White Cloud thalénite-(Y) occurs in two distinct anhedral and botryoidal crystal habits of mostly homogenous composition. In addition, minor secondary thalénite-(Y) is recognized by its distinct Yb-rich composition (up to 0.8 atoms per formula unit (apfu) Yb). Single-crystal X-ray diffraction analysis and structure refinement reveals Y-site ordering with preferential HREE occupation of Y2 vs. Y1 and Y3 REE sites. Chondrite normalization shows continuous enrichment of HREE in White Cloud thalénite-(Y), in contrast to Golden Horn thalénite-(Y) with a slight depletion of the heaviest REE (Tm, Yb and Lu). The results suggest a hydrothermal origin of the Golden Horn miarolitic thalénite-(Y), compared to a combination of both primary magmatic followed by hydrothermal processes responsible for the multiple generations over a range of spatial scales in White Cloud thalénite-(Y).

Arrheniusite-(Ce), CaMg[(Ce7Y3)Ca5](SiO4)3(Si3B3O18)(AsO4)(BO3)F11, a New Member of the Vicanite Group, from the Östanmossa Mine, Norberg, Sweden

2021 ◽  
Author(s):  
Dan Holtstam ◽  
Luca Bindi ◽  
Paola Bonazzi ◽  
Hans-Jürgen Förster ◽  
Ulf B. Andersson
Keyword(s):  
Structure Refinement ◽  
New Mineral ◽  
X Ray Diffraction ◽  
Unit Cell Parameters ◽  
Calculated Density ◽  
Epma Data ◽  
X Ray ◽  
Cell Parameters ◽  
Greenish Yellow ◽  
The Ideal

ABSTRACT Arrheniusite-(Ce) is a new mineral (IMA 2019-086) from the Östanmossa mine, one of the Bastnäs-type deposits in the Bergslagen ore region, Sweden. It occurs in a metasomatic F-rich skarn, associated with dolomite, tremolite, talc, magnetite, calcite, pyrite, dollaseite-(Ce), parisite-(Ce), bastnäsite-(Ce), fluorbritholite-(Ce), and gadolinite-(Nd). Arrheniusite-(Ce) forms anhedral, greenish-yellow translucent grains, exceptionally up to 0.8 mm in diameter. It is optically uniaxial (–), with ω = 1.750(5), ε = 1.725(5), and non-pleochroic in thin section. The calculated density is 4.78(1) g/cm3. Arrheniusite-(Ce) is trigonal, space group R3m, with unit-cell parameters a = 10.8082(3) Å, c = 27.5196(9) Å, and V = 2784.07(14) Å3 for Z = 3. The crystal structure was refined from X-ray diffraction data to R1 = 3.85% for 2286 observed reflections [Fo > 4σ(Fo)]. The empirical formula for the fragment used for the structural study, based on EPMA data and results from the structure refinement, is: (Ca0.65As3+0.35)Σ1(Mg0.57Fe2+0.30As5+0.10Al0.03)Σ1[(Ce2.24Nd2.13La0.86Gd0.74Sm0.71Pr0.37)Σ7.05(Y2.76Dy0.26Er0.11Tb0.08Tm0.01Ho0.04Yb0.01)Σ3.27Ca4.14]Σ14.46(SiO4)3[(Si3.26B2.74)Σ6O17.31F0.69][(As5+0.65Si0.22P0.13)Σ1O4](B0.77O3)F11; the ideal formula obtained is CaMg[(Ce7Y3)Ca5](SiO4)3(Si3B3O18)(AsO4)(BO3)F11. Arrheniusite-(Ce) belongs to the vicanite group of minerals and is distinct from other isostructural members mainly by having a Mg-dominant, octahedrally coordinated site (M6); it can be considered a Mg-As analog to hundholmenite-(Y). The threefold coordinated T5 site is partly occupied by B, like in laptevite-(Ce) and vicanite-(Ce). The mineral name honors C.A. Arrhenius (1757–1824), a Swedish officer and chemist, who first discovered gadolinite-(Y) from the famous Ytterby pegmatite quarry.

scholarly journals Redetermination of Sr2PdO3 from single-crystal X-ray data

2019 ◽  
Vol 75 (1) ◽  
pp. 30-32
Author(s):  
Gohil S. Thakur ◽  
Hans Reuter ◽  
Claudia Felser ◽  
Martin Jansen
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Diffraction Data ◽  
Structure Refinement ◽  
Structure Type ◽  
X Ray Diffraction ◽  
High Quality ◽  
X Ray ◽  
Cell Parameters ◽  
Anisotropic Displacement Parameters

The crystal structure redetermination of Sr2PdO3 (distrontium palladium trioxide) was carried out using high-quality single-crystal X-ray data. The Sr2PdO3 structure has been described previously in at least three reports [Wasel-Nielen & Hoppe (1970). Z. Anorg. Allg. Chem. 375, 209–213; Muller & Roy (1971). Adv. Chem. Ser. 98, 28–38; Nagata et al. (2002). J. Alloys Compd. 346, 50–56], all based on powder X-ray diffraction data. The current structure refinement of Sr2PdO3, as compared to previous powder data refinements, leads to more precise cell parameters and fractional coordinates, together with anisotropic displacement parameters for all sites. The compound is confirmed to have the orthorhombic Sr2CuO3 structure type (space group Immm) as reported previously. The structure consists of infinite chains of corner-sharing PdO4 plaquettes interspersed by SrII atoms. A brief comparison of Sr2PdO3 with the related K2NiF4 structure type is given.

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